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16
Figure 14. Influence of depth on shear capacity.
shear resistance is taken as proportional to the square root of of diagonal compression is at 45 degrees whereas, as these
the cylinder compressive strength f c. Figure 15 presents figures illustrate, axial compression increases the number of
some of the test data by Moody et al. in 1954 (42) from stirrups that carry the shear across diagonal cracks while
which the permissible design stress limit of 2 fc was devel- axial tension decreases the number of stirrups that are avail-
oped. The test beams were typically around 14 inches deep, able to carry the shear across cracks.
overly reinforced in flexure, and contained large aggregates.
Also shown in this plot are the results from a series of tests
by Angelakos in 2001 (43) conducted at the University of 1.2.5 Experimental Test Data
Toronto on larger and more lightly reinforced members cast
The previous examples illustrate the importance of evalu-
using smaller size aggregates. As the results in Figures 14
ating and calibrating any potential simplified provisions with
and 15 show, the apparent safety of the traditional equation
extensive experimental data. Professors Reineck and
for 2 fc as used in U.S. practice for beams without shear
Kuchma (46), and their research assistants have assembled
reinforcement is also dependent on the parameters of beam
what is probably the largest available database of results
depth, concrete strength and maximum aggregate size, not
from shear tests on structural concrete members. The data-
considered in that expression.
base contains more than 2000 test results. This database can
be mined to assess the accuracy and limitation of all prospec-
tive code approaches.
Influence of Axial Loads
The influence of axial compression and tension on shear 1.2.6 Analysis Tools
capacity is examined in Figures 16 (44) and 17 (45). As
shown, traditional U.S. design practice expressions can be In addition to experimental test data, analytical tools can
both conservative and unconservative. Part of the explana- be used to predict the capacity of prestressed and non-
tion for these shortcomings is the assumption that the angle prestressed concrete members. These tools are particularly
